Question

angle of elevation from the top of the tower from two point on the ground at distance a and b unit from the base of the tower and in same straight line with it are complementary .

prove that the height of the tower is root ab unit​

Answer 1

Answer:

h = √ab

Step-by-step explanation:

Let AB be the height of tower h.

Let AP be a and QA = b.

Given that the angles are complementary.

∠APB = θ, Then ∠AQB = 90° - θ.

(i) From ΔBPA,

tanθ = h/a

(ii) From ΔPQA,

⇒ tan(90 - θ) = h/b

⇒ cotθ = h/b.

From (i) & (ii), we get

⇒ tanθ * cotθ = h/a * h/b

⇒ tanθ * (1/tanθ) = h²/ab

⇒ 1 = h²/ab

⇒ h² = ab

⇒ h = √ab.

Hope it helps!

Answer 2

AB is a tower. D and Care two points on the same side of a tower, BD = a and BC = b.

∠ADB and ∠ACB are the complementary angles.

If ∠ADB = x, then ∠ACB = 90 – x

In ∆ADB,………… (1)

In ∆ABC, …………....(2)

Multiplying (1) and (2),

(AB)2 = ab

AB = √ab

Height of tower = AB = √ab

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